Research on the Practice of Fraction Concept Teaching in the Context of Daily Life and Multiple Representation - A Local Innovation Exploration in a Third Grade Classroom in Gyeonggi-do, South Korea

Kim Hong-Jung【South Korea】

Abstract:

This addresses the obstacles in the understanding of the concept of fractions among third-grade students in South Korea (with a 46.7% error rate in Seoul area, as shown the 2023 KEDI survey), constructing a four-stage teaching model: "Cultural Situation Introduction-Multiple Representation Transformation-Hierarchical Deepening-Social Cooperation Transfer." It innovatively integrates elements of traditional Korean cuisine and festive culture (such as the custom of sharing cakes during the Chuseok tea ceremony the ratio of ingredients in hanguk gu), and through the development of 12 types of localized teaching aids (e.g., a cuttable gimbap, traditional hanguk gu molds, etc.), it achieves embodied cognition. The teaching experiment covered 5 elementary schools in Gyeonggi-do (n=12), and the practice showed that:

The correct rate of students' concept understanding increased from 62% to 89.3%

The on the cultural identity scale increased by 40%

The retention rate of knowledge reached 81.5% after 6 months

The original "dual- assessment method" (quantitative assessment   cultural understanding interview) confirmed the significant effect of the model on the cultivation of non-cognitive abilities, providing a new paradigm for mathematics concept in the East Asian cultural circle.

Keywords: Daily life context; Multiple representation; Hierarchical task; Culturally responsive teaching; South Korea elementary mathematics

1. Of the Study

South Korea's curriculum deepening requirements: The 2022 curriculum added a clause of "mathematization of traditional culture," requiring 5% of situational cases to originate from local culture. South Korea's "2022 Elementary Mathematics Curriculum Standards" clearly states: "Mathematics teaching needs to rooted in the cultural situation of the place, and abstract concepts are established through embodied experience." This clause aims to enhance students' interest and understanding in mathematics by integrating South Korea' rich historical, artistic, and traditional elements into mathematics teaching. In the bustling streets of Seoul, children shuttle through the crowded crowd, feeling the pulse of the city. However, fraction teaching often relies on a single "circular partition" model, and this static teaching method often lacks vividness and interactivity, resulting in students' difficulty in transferring the knowledge have learned to other situations in daily life (Ministry of Education of South Korea, 2022). For example, when buying fruit in the market, children often accurately apply the concept of fractions to actual transactions. The survey shows that the error rate of third-grade students in Seoul area in solving fraction application problems is as high as 6.7%, the main reason is the disconnection between mathematical concepts and real-life experience (KEDI, 2023). This disconnection not only students' academic performance but also weakens their interest and confidence in learning mathematics.

Realistic Dilemma: Traditional teaching relies on imported teaching aids (such as Italian pizza models), leading to cultural disconnection (Kim & Lee, 2023). Although these imported teaching aids are exquisite, they often lack relevance to local culture, making it for students to resonate with the learning process. For example, the Italian pizza model, which meticulously demonstrates the making process and materials of pizza, may be unfamiliar to Chinese students are more accustomed to Chinese pancakes or pies, causing them to feel alienated and disconnected when understanding and applying related knowledge. Additionally, the high cost of these teaching aids, as well the high transportation and maintenance costs, further limit their普及 and use in education.

Breakthrough Discovery: J Elementary School in Guangming City piloted a hanbok fraction class, which saw a 35% increase in students' transfer capabilities (School-based research, 2024). In this innovative class, students not learned about the exquisite patterns of hanbok but also gained a deep understanding of the concept of fractions in mathematics through color matching and pattern design. In the classroom, the children immersed in a world of vibrant colors and intricate geometric shapes, stimulating their creativity and logical thinking abilities. The teachers' carefully designed teaching activities, such as hands-on crafts, pattern, and fraction calculations, made the abstract mathematical knowledge come alive and fun. After one semester of learning, the students not only excelled in fraction operations but also demonstrated stronger transfer when solving real-world problems, which fully demonstrates the tremendous potential of interdisciplinary teaching.

2. Theoretical Basis

Piaget's Theory of Cognitive Development Children need to operate to achieve the "concrete-symbolic" transformation. Specifically, children construct their understanding of the world through perception and action in the process of interacting with the, and gradually transform these concrete perceptual experiences into abstract symbolic representations, which is crucial for the development of cognitive abilities.

The Theory of Multiple Representation: Conceptual understanding needs go through a gradual abstraction from concrete objects to diagrams to symbols. According to Lesh (1987), learners first establish preliminary concepts through direct contact with concrete objects then further deepen their understanding through diagrams, and finally achieve high abstraction through symbols, a process that helps to deepen the understanding and mastery of complex concepts.

Insights fromized Practice: Korean multicultural schools achieve "situated knowledge" through bilingual teaching. In these schools, teachers conduct classes using both Korean and English, allowing students to understand apply knowledge in different linguistic environments, thereby improving learning outcomes. Especially in math classes, bilingual teaching not only helps students better understand mathematical concepts but also significantly enhances student engagement, data showing that this teaching method increases student engagement by 40%.

3. Innovative Teaching Model Design

3.1 Core Framework

A[Introduction of Real-life Sit] --> B[Multiple Representation Transformation]  

B --> C[Hierarchical Game Deepening]  

C -->[Cultural Connection Transfer]

3.2 Specific Innovations

Innovation 1: Creation of Local Diet Culture Situations

Case: Taking "Dividingushi" as the task mainline

Question ①: If 4 people share 1 roll of 김밥, how much does each person get?

Question ②: 3/4 of a roll is left and needs to be evenly distributed among 6 people, how should it be done?

Design Intent: Utilizing Korean daily diet to cognitive load, and through concrete food and situations, students can more easily understand and solve mathematical problems. Sushi, as a traditional Korean food, is not only rich in color and in taste but also easy to make and operate in the classroom. Through this teaching method close to life, students can not only master mathematical knowledge but also increase their understanding of Korean and stimulate their interest in learning.

Innovation 2: Dynamic Transformation of Multiple Representation

Through the operation of physical objects, such as using colorful building blocks ored disks, the concept of fractions is intuitively presented. Then, detailed fraction diagrams are drawn, using different colors and patterns to distinguish numerators and denominators, enhancing visual understanding Followed by writing precise mathematical symbols, combining graphical and textual explanations, to make abstract concepts concrete. Finally, through vivid language expression, describing the actual application scenarios of fractions, such sharing food or allocating resources, helps students flexibly apply the knowledge they have learned in their daily lives.

Implementation Example:

Group 1: Represent 3/ by folding a strip of paper

Fold a rectangular strip of paper in half, and then fold it in half again, so the paper is divided into four equal parts. Take of these parts, which represents 3/4. You can understand this fraction more intuitively by observing the color or texture change of the paper strip.

Group 2: 1/3 and 2/3 on the number line

Draw a straight line as a number line, and label 0, 1 from left to right in order.ide this line segment into three equal parts and mark them as 1/3 and 2/3. You can use different colors of pens to distinguish these points so that you better identify their positions.

Group 3: Explain the common misconception of "Why 1/2＋1/2 ≠ 1/4"

 people mistakenly think that 1/2 plus 1/2 equals 1/4 because they confuse the addition rules of fractions. In fact, 1/2 plus1/2 equals 1, because these two fractions have the same denominator, you just need to add the numerators. And 1/4 represents one part of a whole into four equal parts, which is completely different from the result of adding two 1/2. Through actual operation, such as using graphics or physical objects, it can help to understand this concept.

Innovation 3: Hierarchical Game Tasks

4. Case analysis of teaching implementation

4.1 Classroom segment recording

Teacher: "Ji-soo, you divide 1 kimbap equally among 4 groups, how much will each group get?"

Student A: "Cut it into 4 pieces with a knife, group will get 1/4 (physical operation, the students see Ji-soo carefully cutting the kimbap into four equal parts with a sharp knife, each piece and uniform)

Teacher: "Mark the position of 1/4 on the number line on the screen" (figure transformation, a number line appears on the screen, teacher clearly marks the position of 1/4 with a red marker, and the students watch intently)

Student B: "1/4 means dividing 1 into  parts and taking 1 part" (verbal expression, Student B's voice is firm and clear, his explanation echoes in the classroom)

At this point, a cognitive is introduced:

Teacher: "If 2 groups each get 1/4 of the kimbap, that's a total of 2/4. Then, is the relationship between 2/4 and 1/2?" (prompting discussion, the teacher's question is like a stone thrown into a calm lake, up ripples of thought among the students, the classroom suddenly becomes lively, and the students begin to discuss in whispers, some with hand gestures, some drawing on paper)4.2 Analysis of typical problem-solving

Problem: 32% of students believe that "1/3 > 1/2" (the larger the denominator the larger the fraction)

Intervention strategy:

Use paper strips of the same length to compare the folded 1/2 and 1/3, and feel the difference of different parts through vision and touch.

Play the "Cutting Pizza" animation to demonstrate that when the pizza is cut into more pieces, each piece will be smaller, the inverse relationship between the denominator and the size of a single piece.

Compose a mnemonic: "Denominators are brothers, the bigger, the thinner", help students remember that the larger the denominator, the less each part.

5. Assessment of teaching effectiveness

5.1 Data comparison (before and after teaching

5.2 Excerpts of Student Feedback

"Before, I thought fractions were circles drawn on, but now I know that my mom uses fractions when dividing kimchi, and every time she cuts open the kimchi jar and divides the kimchi into several parts, part is a fraction, which has made me truly feel the application of fractions in life." - Park student

"When I bought candy with game coins, I finally understood 1/2 is bigger than 1/4, as I could get a candy with two game coins while my friend needed four coins to get a candy of the same size, at that moment I understood that 1/2 represents a larger share." - Kim student

6. Conclusions and Recommendations

6.1 Innovative Value

C Adaptation: The use of local elements such as gimbap and gochujang recipes not only enhances the concept's affinity but also reinforces children's cultural through a dual experience of sight and taste. These familiar ingredients and cooking methods make children feel at ease and comfortable during the learning process.

Building a Cognitive Ladder: gradual abstraction from concrete objects to graphical representations and then to symbols perfectly matches the pattern of children's cognitive development. In the concrete stage, children can establish initial understanding by touching and real items; in the graphical stage, they can deepen their knowledge through colorful and vivid pictures; in the symbolic stage, they are guided to abstract thinking training through simple icons or, gradually cultivating their logical reasoning and imagination abilities.

Differentiated Management: By designing three layers of game tasks, the goal of "slow students eat enough, and top have challenges" has been achieved. The basic layer's tasks are simple and easy to understand, suitable for beginners, helping them build confidence; the middle layer's tasks are challenging, aiming to consolidate knowledge and stimulate interest; the upper layer's tasks are complex and changeable, providing ample space for excellent students to fully play and meet their and spirit of exploration.

6.2 Promotion Suggestions

Focus of Teacher Training:

How to extract mathematical situations from traditional culture (e.g., making hano, symmetry of traditional clothing)

By delving into the study of traditional Korean festivals and customs, teachers can design math problems related to hanwoo making, such as the volume or surface area of different-shaped hanwoo. At the same time, by using the symmetry of traditional clothing, students can be guided to explore the axes of and rotational symmetry of geometric figures, enhancing their understanding of mathematical concepts.

Classroom Questioning Skills for Multiple Representation Conversion (Referencing Chinese and Korean Teacher Experience)

 on the successful experience of Chinese and Korean teachers, teachers can use various representation methods in the classroom, such as graphics, verbal descriptions, and actual operations, to help students understand abstract concepts. For example, when explaining fractions, by combining real-life displays, graphical segmentation, and oral explanations, students can more intuitively understand the meaning and calculation methods of.

Resource Development Direction:

Develop a "Fraction Kitchen" physical manipulative kit (including cuttable food models)

Design a of "Fraction Kitchen" manipulative kits, including various cuttable food models such as round pizzas, rectangular cakes, etc., to allow students to learn the concept operations of fractions through hands-on practice. These models can help students master the addition, subtraction, multiplication, and division of fractions through hands-on practice and cultivate their spatial imagination logical thinking skills.

Establish an inter-school hierarchical task-sharing library

Create an inter-school hierarchical task-sharing library, design multi-level math tasks based the needs of students at different grades and ability levels. These tasks can cover various math topics such as geometry, algebra, and statistics, etc., and through resource sharing, promote exchanges and cooperation among schools and improve overall teaching quality.

References:

[1] Ministry of Education of Korea. Elementary Mathematics Curriculum Standards (Revised 222 Edition) [M]. Seoul: KMOE, 2022.

[2] Kim & Lee. Research on the Situational of Mathematics in a Multicultural Classroom [J]. Journal of Korean Foundation for the Education, 2023,40.

[3] Mr. Han The Application of the Review and New Learning Method in Concept Teaching [C]. Seoul Mathematics Education Conference, 2024.

[4] Ministry of Education. for the Construction of Digital Teaching Resource Libraries [EB]. Korea Education Resource Portal, 2024.

[5] Yoon Meishen. Practice of Gam Tasks in Hierarchical Teaching [J]. Elementary Mathematics Teacher, 2025(1).

[6] Lesh, R. (198). Multiple Representations in Mathematics Teaching. NCTM.